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Mathematics

Mathematics and System Engineering Faculty Publications

2009

Articles 1 - 13 of 13

Full-Text Articles in Physical Sciences and Mathematics

Solutions Of A System Of Integral Equations In Orlicz Spaces, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong Dec 2009

Solutions Of A System Of Integral Equations In Orlicz Spaces, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong

Mathematics and System Engineering Faculty Publications

We consider the following system of integral equations Ui(t) = ∫1gi(t,s)fi(s,u1(s),u2(s),...,un(s))ds, a.e. t [0,1], 1 ≤ i ≤ n. Our aim is to establish criteria such that the above system has a solution (u±,U2,... ,un) where uiLφ (Orlicz space), 1 < i < n. We further investigate the system Ui(t) = ∫1gi(t,s)fi(s,u1(s),u2(s),...,un(s))ds, a.e. t [0,1], 1 ≤ i ≤ n. and establish the existence of constant-sign solutions in Orlicz spaces, i.e., for each 1 ≤ i ≤ n, Oui > 0 and ui G L

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Complementary Lidstone Interpolation And Boundary Value Problems, Ravi P. Agarwal, Sandra Pinelas, Patricia J.Y. Wong Nov 2009

Complementary Lidstone Interpolation And Boundary Value Problems, Ravi P. Agarwal, Sandra Pinelas, Patricia J.Y. Wong

Mathematics and System Engineering Faculty Publications

We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial P 2m (t) of degree 2m, which involves interpolating data at the odd-order derivatives. For P 2m (t) we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a (2m+1) th order …

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An Approximation Approach To Eigenvalue Intervals For Singular Boundary Value Problems With Sign Changing And Superlinear Nonlinearities, Haishen Lu, Ravi P. Agarwal, Donal O'Regan Oct 2009

An Approximation Approach To Eigenvalue Intervals For Singular Boundary Value Problems With Sign Changing And Superlinear Nonlinearities, Haishen Lu, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

This paper studies the eigenvalue interval for the singular boundary value problem u″ = g (t, u) + λ h (t, u), t ∈(0, 1),u (0) = 0 = u (1), where g + h may be singular at u = 0, t = 0, 1, and may change sign and be superlinear at u = + ∞. The approach is based on an approximation method together with the theory of upper and lower solutions. Copyright © 2009 Haishen Lü et al.

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Super-Relaxed (Η)-Proximal Point Algorithms, Relaxed (Η)-Proximal Point Algorithms, Linear Convergence Analysis, And Nonlinear Variational Inclusions, Ram U. Verma, Ravi P. Agarwal Sep 2009

Super-Relaxed (Η)-Proximal Point Algorithms, Relaxed (Η)-Proximal Point Algorithms, Linear Convergence Analysis, And Nonlinear Variational Inclusions, Ram U. Verma, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We glance at recent advances to the general theory of maximal (set-valued) monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed (η)-proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion of maximal (η)-monotonicity. Investigations highlighted in this communication are greatly influenced by the celebrated work of Rockafellar (1976), while others have played a significant part as well in generalizing the proximal point algorithm considered by Rockafellar (1976) to the case of the …

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Existence Of Pseudo Almost Automorphic Solutions For The Heat Equation With Sp-Pseudo Almost Automorphic Coefficients, Toka Diagana, Ravi P. Agarwal Aug 2009

Existence Of Pseudo Almost Automorphic Solutions For The Heat Equation With Sp-Pseudo Almost Automorphic Coefficients, Toka Diagana, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We obtain the existence of pseudo almost automorphic solutions to the N-dimensional heat equation with Sp-pseudo almost automorphic coefficients.

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Fixed Point Theory For Admissible Type Maps With Applications, Ravi P. Agarwal, Donal O'Regan Jul 2009

Fixed Point Theory For Admissible Type Maps With Applications, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

We present new Leray-Schauder alternatives, Krasnoselskii and Lefschetz fixed point theory for multivalued maps between Fréchet spaces. As an application we show that our results are directly applicable to establish the existence of integral equations over infinite intervals. Copyright © 2009 R. P. Agarwal and D. O'Regan

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Weighted Composition Operators From Logarithmic Bloch-Type Spaces To Bloch-Type Spaces, Stevo Stevic, Ravi P. Agarwal Jul 2009

Weighted Composition Operators From Logarithmic Bloch-Type Spaces To Bloch-Type Spaces, Stevo Stevic, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

The boundedness and compactness of the weighted composition operators from to Bloch-type spaces are studied here. © 2009 S. Stević and R. P. Agarwal.

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Oscillation Criteria For Second-Order Forced Dynamic Equations With Mixed Nonlinearities, Ravi P. Agarwal, Agacik Zafer Jun 2009

Oscillation Criteria For Second-Order Forced Dynamic Equations With Mixed Nonlinearities, Ravi P. Agarwal, Agacik Zafer

Mathematics and System Engineering Faculty Publications

We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r(t) Φα (xΔ))Δ + f (t, xσ) = e(t), t ∈ [t0, ∞) T with f(t, x) = q(t)Φα(x) + ∑i=1nqi(t)Φβi (x), Φ* (u) = u *-1u, where [t0, ∞)T is a time scale interval with t0 ∈ T, the functions r, q, qi, e: [t0, ∞)T → ℝ are right-dense continuous with r > 0, σ is the forward jump operator, xσ(t) := x (σ(t)), and β1 > ⋯ > βm > α > βm+1 > ⋯ βn > 0. All results obtained are new even for …

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A Survey On Semilinear Differential Equations And Inclusions Involving Riemann-Liouville Fractional Derivative, Ravi P. Agarwal, Mohammed Belmekki, Mouffak Benchohra Feb 2009

A Survey On Semilinear Differential Equations And Inclusions Involving Riemann-Liouville Fractional Derivative, Ravi P. Agarwal, Mohammed Belmekki, Mouffak Benchohra

Mathematics and System Engineering Faculty Publications

We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative. Our approach is based on the C0-semigroups theory combined with some suitable fixed point theorems.

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Constant Sign And Nodal Solutions For Problems With The P-Laplacian And A Nonsmooth Potential Using Variational Techniques, Ravi P. Agarwal, Michael E. Filippakis, Donal O'Regan, Nikolaos S. Papageorgiou Jan 2009

Constant Sign And Nodal Solutions For Problems With The P-Laplacian And A Nonsmooth Potential Using Variational Techniques, Ravi P. Agarwal, Michael E. Filippakis, Donal O'Regan, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

We consider a nonlinear elliptic equation driven by the p-Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one positive, the second negative, and the third sign changing (nodal solution). Our hypotheses onthe nonsmooth potential incorporate in our framework of analysis the so-called asymptotically p-linear problems.

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Maintenance In Single-Server Queues: A Game-Theoretic Approach, Najeeb Al-Matar, Jewgeni H. Dshalalow Jan 2009

Maintenance In Single-Server Queues: A Game-Theoretic Approach, Najeeb Al-Matar, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

We use antagonistic stochastic games and fluctuation analysis to examine a single-server queue with bulk input and secondary work during server's multiple vacations. When the buffer contents become exhausted the server leaves the system to perform some diagnostic service of a minimum of jobs clustered in packets of random sizes (event A). The server is not supposed to stay longer than units of time (event B). The server returns to the system when A or B occurs, whichever comes first. On the other hand, he may not break service of a packet in a middle even if A or B …

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Generalized First-Order Nonlinear Evolution Equations And Generalized Yosida Approximations Based On H-Maximal Monotonicity Frameworks, Ram U. Verma Jan 2009

Generalized First-Order Nonlinear Evolution Equations And Generalized Yosida Approximations Based On H-Maximal Monotonicity Frameworks, Ram U. Verma

Mathematics and System Engineering Faculty Publications

First a general framework for the Yosida approximation is introduced based on the relative H-maximal monotonicity model, and then it is applied to the solvability of a general class of first-order nonlinear evolution equations. The obtained results generalize and unify a wide range of results to the context of the solvability of first-order nonlinear evolution equations in several settings.© 2009 Texas State University-San Marcos.

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Advanced Discrete Halanay-Type Inequalities: Stability Of Difference Equations, Ravi P. Agarwal, Youngho Kim, Syamal K. Sen Jan 2009

Advanced Discrete Halanay-Type Inequalities: Stability Of Difference Equations, Ravi P. Agarwal, Youngho Kim, Syamal K. Sen

Mathematics and System Engineering Faculty Publications

We derive new nonlinear discrete analogue of the continuous Halanay-type inequality. These inequalities can be used as basic tools in the study of the global asymptotic stability of the equilibrium of certain generalized difference equations.

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